- Title
- Epigraphical and uniform convergence of convex functions
- Creator
- Borwein, Jonathan M.; Vanderwerff, Jon D.
- Relation
- Transactions of the American Mathematical Society Vol. 348, Issue 4, p. 1617-1631
- Publisher Link
- http://dx.doi.org/10.1090/S0002-9947-96-01581-4
- Publisher
- American Mathematical Society (AMS)
- Resource Type
- journal article
- Date
- 1996
- Description
- We examine when a sequence of lsc convex functions on a Banach space converges uniformly on bounded sets (resp. compact sets) provided it converges Attouch-Wets (resp. Painlevé-Kuratowski). We also obtain related results for pointwise convergence and uniform convergence on weakly compact sets. Some known results concerning the convergence of sequences of linear functionals are shown to also hold for lsc convex functions. For example, a sequence of lsc convex functions converges uniformly on bounded sets to a continuous affine function provided that the convergence is uniform on weakly compact sets and the space does not contain an isomorphic copy of ℓ₁
- Subject
- epi-convergence; lsc convex function; uniform convergence; pointwise convergence; Attouch-Wets convergence; Painlevé-Kuratowski convergence; Mosco convergence
- Identifier
- http://hdl.handle.net/1959.13/940410
- Identifier
- uon:13002
- Identifier
- ISSN:0002-9947
- Rights
- First published in Transactions of the American Mathematical Society in Vol.348, No. 4, pp.1617-1631, 1996, published by the American Mathematical Society
- Language
- eng
- Full Text
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|---|---|---|---|---|---|---|---|
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